Evil Minions are the non combat version of Mooks. They tend to the villain's science labs, clean up the corpses from the shark pools, give The Dragon stress relief via being choked or other dog kickery, and generally run around like headless chickens when the hero pushes the Big Red Button.

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One of the more classic examples are the white helmeted technicians alongside the Imperial Stormtroopers of the Star Wars movies, as well as the Trade Federation droid bridge crews from the prequel series.

The bad guy scientist in Resident Evil 3: Extinction gleefully leaves two fawning lab assistants to be killed by his enhanced zombie when it goes on a rampage. True, one was dead meat, but the other he could have saved.

Many classic James Bond villains have bunches of these guys to man the Supervillain Lair and control the orbital death rays or ICBM-hijacking equipment or what have you.

Subverted somewhat in the Whateley Universe. At the Super-Hero School Whateley Academy, there is a clique of rich kids who happen to also be mutants. At one meeting, a number of them get into a discussion of the problems with hiring minions and maintaining an effective corps of dangerous minions. They all think of this as if they were hiring middle managers or highly competitive salesmen or grouchy programmers. Of course, the school handbook has an entire section on rules to follow if you hire other students as your minions...

The novel Death Star which is all about the evil and not-so-evil minions on the titular space station.

Gilina on Farscape was an Evil Minion to the Peacekeepers, serving as a technician in her debut episode "Peace Keeper Tech Girl". Her romantic feelings for John got her upgraded to Mauve Shirt, and later she did a Mook Face Turn out of that love.

The game Evil Genius has an entire tree of combat Mooks and non-combat Evil Minions, all descended from the basic Worker. They're distinct from "Henchmen" who are more powerful, named, controllable by the player and have to be hired. The game is interesting in that it gives each Minion a name and mini biography, has loyalty traits, and can be killed on a whim by the evil genius to inspire fear and loyalty in nearby minions. While the low ranking ones are eminently expendable, ones higher up on the job tree can get to be as or more valuable than Henchmen if a raid reduces their numbers.

The Imps in Dungeon Keeper, who excavate and expand your dungeons as well as the Trolls, who are your mechanics who build traps and such.

The Minions in Overlord are a literal example of this, though they're all your combat Mooks save for the NPC ones like Gnarl or Quaver.

Giblet, the Foregemaster, or the women you kidnap from Spree maybe be examples.

In Sluggy Freelance, when Aylee (actually her clone) started her own web design business in league with Hereti Corp, there were a number of regular web designers working there. These minions served a twofold purpose: 1) keep the legitimate stream of revenue flowing, and 2) be a handy source of human snacks for Aylee.

Later on, Hereti Corp blurred the line between Mook and Minion when they opened their own chain of pizza places, but still staffed the restuarants with their black ops mercenaries (or at least gave the staff the same all-black uniforms).

Henchman For Hire seems to play this in a comedic way in addition to playing various other super villain and minion tropes

The villains in Batman's and Superman's animated series were constantly hiring minions, usually ones that reflected that villain's particular motif.

Notably, it became something of a plot point that the Joker had trouble finding Minions both because Batman kept kicking his ass, and also because he's a Bad Boss.

Also turns up in the comics, and sometimes gets parodied / lampshaded with the mooks talking about times they were working for other villains.

Parodied in the show Word Girl. Doctor Two-Brains (who has the brain of a super-intelligent lab rat stuck on his head) has two (dumb as dirt) minions. (They normally start out conversations with saying "Hey, Boss?" and Two-Brains responding "Yes, minions?") They normally wear jump-suits with a rat logo on them, but in one episode when they complained about their outfits, Two-Brains decided to put them in mascot outfits made to look like mice.

One of them, the taller of the two, never speaks, the other speaks, and wears a hat (forgot it's name) Under that had is a ridiculous, seventies-ish style haircut he is proud of. Dr. Twobrains turned it into CREAM CHEESE!! Just to show them how his raygun works!